For about $12, Sprint will soon let subscribers buy a wireless plan that only connects to Facebook.

For that same price, they could choose instead to connect only with Twitter, Instagram or Pinterest—or for $10 more, enjoy unlimited use of all four. Another $5 gets them unlimited streaming of a music app of their choice.

The plan, offered under the company’s Virgin Mobile brand of prepaid service, comes as wireless carriers are experimenting with ways to make wireless Internet access more affordable for the poorest consumers by offering special deals on slices of the Web.

In the process, however, they are testing the long-held principle that all Internet traffic should be treated equally by creating strong incentives for subscribers to use already dominant services.

In June, T-Mobile US Inc. TMUS -0.03% said it would allow customers unlimited use of mobile streaming music that doesn’t count against their data plans when they use services like Pandora and Spotify. Earlier this year, AT&T Inc. T +2.64% created a program allowing companies to foot the bill for data used by their customers on mobile apps.

Sprint said the plan—called Virgin Mobile Custom—was aimed at giving consumers more choices.

“This is really just part of a broader effort toward customization,” said Dow Draper, president of prepaid at Sprint. Instead of buying a bucket of data, customers can now pay less for just the app they use the most, he said.

Other apps might be added in the future, he said. For now, customers can only choose between those four apps, and they’d need a data plan in order to access anything else. The apps were chosen by Sprint because they’re the most heavily used.

Sprint isn’t being paid by any of the apps, but Mr. Draper didn’t rule it out in the future. “It’s definitely possible,” he said. “But we have not gone down that path yet.”

The new plan is only available at Wal-Mart and the base offering covers just 20 minutes of talk time and 20 texts. Subscribers can customize the plan by buying up to unlimited talk or text or both, and by choosing among data packages.

Each line starts at $6.98 a month. Unlimited service on Facebook, Twitter, Instagram or Pinterest costs another $5, or another $15 for all four.

The service also includes a feature that allows parents to restrict which apps children can use on the phones.